Convolutional Neural Networks for different-sized Source and Target
Yes actually. There have been quite a few different adaptations to convolutional neural networks to do precisely what you are describing. 

Here is an earlier one. See section 3.2.5

Here He et al. create a method known as Spatial Pyramid Pooling(SPP). In this method, you are able construct a fixed length representation regardless of input size by pooling them into "spatial bins" which are proportional to the input size, and thusly do not need to modify input dimensions.

There are a few newer methods that improve on this in various capacities, as usual, your solution will be dependent on the problem and other situation-dependent constraints. I suggest you dig deeper into the literature to find the optimal solution in your case.